Replacing a transistor with a compound transistor

As a result of their better overall performance in certain transistor circuits, Darlington pairs and compound transistors are often used to replace a single transistor. The authors consider the consequences of such a replacement on the circuit´s DC behavior with respect to the number of operating points. They prove that if a circuit due to its topology alone possessed a unique operating point, then replacing any number of single transistors with Darlington transistor pairs (or with compound transistors, under specified conditions) produces a new circuit which also has a unique operating point.